Glossary: F - L

Fermi surface

According to the Pauli exclusion principle, it is not possible for identical fermions to occupy the same quantum state. In a system with many identical fermions, such as electrons in a metal, the fermions fill in the available quantum states in order of increasing energy. The energy of the highest occupied quantum state defines the energy of the Fermi surface, which is a surface of constant energy in momentum space.

fermion

A fermion is a particle with half-integer spin. The quarks and leptons of the Standard Model are fermions with a spin of 1/2. Composite particles can also be fermions. Baryons, such as protons and neutrons, and atoms of the alkali metals are all fermions. See: alkali metal, baryon, boson, lepton, spin.

ferromagnet

A ferromagnet is a magnet in which the microscopic magnetic moments inside the material all point in the same direction. Most magnetic materials we encounter in daily life are ferromagnets.

field

In general, a field is a mathematical function that has a value (or set of values) at all points in space. Familiar examples of classical fields are the gravitational field around a massive body and the electric field around a charged particle. These fields can change in time, and display wave-like behavior. In quantum field theory, fields are fundamental objects, and particles correspond to vibrations or ripples in a particular field.

fitness landscape

The fitness landscape is a visual representation of how well adapted different genotypes are to a set of environmental conditions. Each possible genotype occupies a point on the landscape. The distance between each pair of genotypes is related to how similar they are, and the height of each point indicates how well adapted that genotype is.

flavor

In particle physics, the flavor of a particle is a set of quantum numbers that uniquely identify the type of particle it is. The quark flavors are up, down, charm, strange, top, and bottom. The lepton flavors are electron, muon, tau, and their corresponding neutrinos. A particle will have a flavor quantum number of +1 in its flavor, and its antiparticle has a quantum number of -1 in the same flavor. For example, an electron has electron flavor +1, and a positron has electron flavor of -1.

force carrier

In quantum field theory, vibrations in the field that correspond to a force give rise to particles called force carriers. Particles that interact via a particular force do so by exchanging these force carrier particles. For example, the photon is a vibration of the electromagnetic field and the carrier of the electromagnetic force. Particles such as electrons, which have negative electric charge, repel one another by exchanging virtual photons. The carrier of the strong force is the gluon, and the carrier particles of the weak force are the W and Z bosons. Force carriers are always bosons, and may be either massless or massive.

frequency comb

A frequency comb is a special type of laser that has a spectrum that looks like a comb. Most lasers emit light at one well-defined frequency, and have a resonance curve that looks like a peak at that frequency and zero everywhere else. A frequency comb has a resonance curve that looks like a series of evenly spaced peaks over a broad range. These lasers were important in the development of optical clocks because the peaks in their spectrum are at optical frequencies, but the spacing between peaks is at much lower microwave frequencies. Comb lasers therefore provide a link between optical frequencies that are very difficult to measure directly, and microwave frequencies that can be counted with well-established laboratory techniques.

frustrated

A physical system is frustrated if it has no well-defined ground state because there are competing interactions among the pieces of the system that cannot simultaneously be at an energy minimum. A simple example is a system of three spins. If the interaction energy between two spins is lowest when they point in opposite directions, the ground state of a pair of spins is clearly for the two spins to point in opposite directions. If a third spin is added, it is pulled in opposite directions attempting to minimize its interaction with the other two.

galaxy cluster

A galaxy cluster is a group of galaxies bound together by the force of gravity. Like the planets in our solar system, galaxies in a cluster orbit a common center of mass. However, galaxies execute more complicated orbits than the planets because there is no massive central body in the cluster playing the role of the Sun in our solar system. Galaxy clusters typically contain a few hundred galaxies, and are several megaparsecs (ten million light-years) in size. The orbital velocities of galaxies in clusters provide strong evidence for dark matter.

gamma rays

Gamma rays are high-energy photons that are sometimes emitted from the nucleus of an atom that has just decayed by emitting an alpha or a beta particle. Gamma ray photons typically have energies greater than 1 MeV. They are on the high-energy end of the electromagnetic spectrum.

general relativity

General relativity is the theory Einstein developed to reconcile gravity with special relativity. While special relativity accurately describes the laws of physics in inertial reference frames, it does not describe what happens in an accelerated reference frame or gravitational field. Since acceleration and gravity are important parts of our physical world, Einstein recognized that special relativity was an incomplete description and spent the years between 1905 and 1915 developing general relativity. In general relativity, we inhabit a four-dimensional spacetime with a curvature determined by the distribution of matter and energy in space. General relativity makes unique, testable predictions that have been upheld by experimental measurements, including the precession of Mercury's orbit, gravitational lensing, and gravitational time dilation. Other predictions of general relativity, including gravitational waves, have not yet been verified. While there is no direct experimental evidence that conflicts with general relativity, the accepted view is that general relativity is an approximation to a more fundamental theory of gravity that will unify it with the Standard Model. See: gravitational lensing. gravitational time dilation, gravitational wave, precession, spacetime, special relativity, Standard Model.

genome

An organism's genome is the complete set of genetic information required to reproduce and maintain that organism in a living state.

gluons

Gluons are particles in the Standard Model that mediate strong interactions. Because gluons carry color charge, they can participate in the strong interaction in addition to mediating it. The term "gluon" comes directly from the word glue, because gluons bind together into mesons.

gravitational lensing

Gravitational lensing occurs when light travels past a very massive object. According to Einstein's theory of general relativity, mass shapes spacetime and space is curved by massive objects. Light traveling past a massive object follows a "straight" path in the curved space, and is deflected as if it had passed through a lens. Strong gravitational lensing can cause stars to appear as rings as their light travels in a curved path past a massive object along the line of sight. We observe microlensing when an object such as a MACHO moves between the Earth and a star. The gravitational lens associated with the MACHO focuses the star' light, so we observe the star grow brighter then dimmer as the MACHO moves across our line of sight to the star.

gravitational mass

The gravitational mass of a particle is the gravitational equivalent of electric charge: the physical property of an object that causes it to interact with other objects through the gravitational force. According to the equivalence principle, gravitational mass is equivalent to inertial mass. See: equivalence principle, inertial mass.

gravitational time dilation

Clocks in a strong gravitational field run slower than clocks in a weaker gravitational field. This effect, predicted by Einstein's theory of general relativity and confirmed by precision experiments both on Earth and in space, is called "gravitational time dilation."

gravitational waves

Gravitational waves are oscillations of a gravitational field, just as light waves are oscillations of an electromagnetic field. Predicted by general relativity, gravitational waves travel at the speed of light and have transverse polarization. It is difficult to detect gravitational waves directly because their amplitude is so small, but their effect on the binary pulsar system discovered by Hulse and Taylor provides indirect evidence of their existence.

gravitino

The gravitino is the superpartner of the graviton. See: superpartner, supersymmetry.

graviton

The graviton is the postulated force carrier of the gravitational force in quantum theories of gravity that are analogous to the Standard Model. Gravitons have never been detected, nor is there a viable theory of quantum gravity, so gravitons are not on the same experimental or theoretical footing as the other force carrier particles.

gravity

Gravity is the least understood of the four fundamental forces of nature. Unlike the strong force, weak force, and electromagnetic force, there is no viable quantum theory of gravity. Nevertheless, physicists have derived some basic properties that a quantum theory of gravity must have, and have named its force-carrier particle the graviton.

ground state

The ground state of a physical system is the lowest energy state it can occupy. For example, a hydrogen atom is in its ground state when its electron occupies the lowest available energy level.

group

Group is a mathematical term commonly used in particle physics. A group is a mathematical set together with at least one operation that explains how to combine any two elements of the group to form a third element. The set and its operations must satisfy the mathematical properties of identity (there is an element that leaves other group elements unchanged when the two are combined), closure (combining any two group elements yields another element in the group), associativity (it doesn't matter in what order you perform a series of operations on a list of elements so long as the order of the list doesn't change), and invertability (every operation can be reversed by combining the result with another element in the group). For example, the set of real numbers is a group with respect to the addition operator. A symmetry group is the set of all transformations that leave a physical system in a state indistinguishable from the starting state.

hadron

The term hadron refers to the Standard Model particle made of quarks. Mesons and baryons are classified as hadrons.

handedness

Handedness, also called "chirality," is a directional property that physical systems may exhibit. A system is "right handed" if it twists in the direction in which the fingers of your right hand curl if your thumb is directed along the natural axis defined by the system. Most naturally occurring sugar molecules are right handed. Fundamental particles with spin also exhibit chirality. In this case, the twist is defined by the particle's spin, and the natural axis by the direction in which the particle is moving. Electrons produced in beta-decay are nearly always left handed.

harmonic oscillator

A harmonic oscillator is a physical system that, when displaced from equilibrium, experiences a restoring force proportional to the displacement. A harmonic oscillator that is displaced and then let go will oscillate sinusoidally. Examples from classical physics are a mass attached to a spring and a simple pendulum swinging through a small angle.

harmonic trap

A harmonic trap is a trap in which the trapped objects (e.g., atoms) are pushed toward the center of the trap with a force proportional to their distance from the center of the trap. The motion of particles in a harmonic trap is analogous to the motion of a mass attached to a spring around the spring's equilibrium position. It is convenient to use harmonic traps in experiments because it is straightforward to calculate the motion of particles in analogy to the mass on a spring.

Heisenberg uncertainty principle

The Heisenberg uncertainty principle states that the values of certain pairs of observable quantities cannot be known with arbitrary precision. The most well-known variant states that the uncertainty in a particle's momentum multiplied by the uncertainty in a particle's position must be greater than or equal to Planck's constant divided by 4. This means that if you measure a particle's position to better than Planck's constant divided by 4, you know that there is a larger uncertainty in the particle's momentum. Energy and time are connected by the uncertainty principle in the same way as position and momentum. The uncertainty principle is responsible for numerous physical phenomena, including the size of atoms, the natural linewidth of transitions in atoms, and the amount of time virtual particles can last.

Hertz

Hertz (Hz) is a unit of frequency, defined as the number of complete cycles of a periodic signal that take place in one second. For example, the frequency of sound waves is usually reported in units of Hertz. The normal range of human hearing is roughly 20–20,000 Hz. Radio waves have frequencies of thousands of Hz, and light waves in the visible part of the spectrum have frequencies of over 1014 Hz.

hierarchy problem

The hierarchy problem in theoretical physics is the fact that there appear to be two distinctly different energy scales in the universe for reasons that are not understood. The first energy scale, called the "electroweak scale," is associated with everything except gravity. The electroweak scale is set by the mass of the W and Z bosons at around 100 GeV, and determines the strength of the strong, electromagnetic, and weak interactions. The second is the Planck scale, at 1019 GeV, which is associated with gravitational interactions. Another way of stating the hierarchy problem is to ask why gravity is 39 orders of magnitude weaker than the other fundamental forces of nature.

Higgs boson

The Higgs boson is a Standard Model particle thought to give particles their mass. Light particles interact less strongly with the Higgs than heavy particles. As of 2010, it had not yet been discovered. If the Higgs exists, experiments at LEP and the Tevatron have determined that its mass cannot be smaller than 110 GeV, and cannot lie between 163 and 166 GeV.

Higgs mechanism

The Higgs mechanism, named for Peter Higgs but actually proposed independently by several different groups of physicists in the early 1960s, is a theoretical framework that explains how fundamental particles acquire mass. The Higgs field underwent a phase transition as the universe expanded and cooled, not unlike liquid water freezing into ice. The condensed Higgs field interacts with the different massive particles with different couplings, giving them their unique masses. This suggests that particles that we can measure to have various masses were massless in the early universe. Although the Higgs mechanism is an internally consistent theory that makes successful predictions about the masses of Standard Model particles, it has yet to be experimentally verified. The clearest signature of the Higgs mechanism would be the detection of a Higgs boson, the particle associated with vibrations of the Higgs field.

Hubble constant

The Hubble constant, defined as "the ratio of the present rate of expansion to the current size of the universe," is a measure of the expansion of the universe. Measurements of Cepheid variable stars made using the Hubble Space Telescope give the present value of the Hubble constant as 72 3 kilometers per second per megaparsec. See: Hubble diagram, megaparsec, parsec.

Hubble diagram

The Hubble diagram is a graph that compares the brightness (or distance) of objects observed in the universe to their redshift (or apparent recessional velocity). Edwin Hubble, for whom the diagram is named, plotted his observations of galaxies outside the Milky Way in this format. In doing so, Hubble showed that the universe is expanding because the recessional velocities of the galaxies are proportional to their distances. Modern Hubble diagrams are based on observations of Type Ia supernovae, and suggest that the expansion rate of the universe is increasing.

Hubble's Law

Hubble's Law states that the redshift, or apparent recessional velocity, of a distant galaxy is equal to a constant called "Hubble's constant" times the distance to the galaxy. See: Hubble's constant, Hubble diagram, megaparsec, parsec.

hyperfine interaction

When the nucleus of an atom has a non-zero magnetic moment, the magnetic field of the nucleus interacts with electrons in the atom. This interaction is called the hyperfine interaction, and leads to finely spaced atomic energy levels called hyperfine structure.

hyperfine structure

When the nucleus of an atom has a nonzero magnetic moment, some of the energy levels that electrons can occupy in the atom are very finely spaced. The arrangement of these finely spaced levels is called "hyperfine structure." The difference in energy between hyperfine levels typically corresponds to a microwave photon frequency or light with a wavelength on the order of centimeters. The energy levels in the cesium atom used to define the second are hyperfine levels.

imaginary number

An imaginary number is a real number multiplied by the square root of -1, which is denoted by i.

index of refraction

A material's index of refraction is defined as the speed that light travels in the material divided by the speed of light in a vacuum. Therefore, the index of refraction of the vacuum is equal to one. Light slows down as it enters a material due to the interaction between the oscillating electric and magnetic fields of the light wave and the constituent parts of the material. The index of refraction of air is 1.003, and the index of refraction of water is 1.33.

inelastic neutron scattering

Inelastic neutron scattering is an experimental technique for studying various properties of materials. A beam of neutrons of a particular energy is shot at a sample at a particular angle with respect to the crystal lattice. The energy of neutrons scattered by the sample is recorded, and the experiment is repeated at different angles and beam energies. The scattered neutrons lose some of their energy to the sample, so the scattering is inelastic. The results of inelastic neutron scattering are readily interpreted in terms of the wave nature of particles. The incident neutron beam is a wave with a frequency proportional to the neutron energy. The crystal preferentially absorbs waves with frequencies that correspond to its natural modes of vibration. Note that the vibrations can be magnetic or acoustic. Thus, the modes of the sample can be inferred by mapping out how much energy is absorbed from the incident beam as a function of the incident beam energy. Inelastic neutron scattering has also been used to study acoustic oscillations and their corresponding quasiparticles in liquids.

inertial mass

Inertia is the measure of an object's reluctance to accelerate under an applied force. The inertial mass of an object is the mass that appears in Newton's second law: the acceleration of an object is equal to the applied force divided by its inertial mass. The more inertial mass an object has, the less it accelerates under a fixed applied force. See: equivalence principle, gravitational mass.

inflation

Inflation is a period of exponential expansion thought to have occurred around 10-36 seconds after the universe began. During this period, which lasted for a few million Planck times, the universe expanded by a factor of at least 1025, smoothing out temperature and density fluctuations to produce the nearly uniform universe we observe today. Although the mechanism driving inflation is still not understood, evidence from the cosmic microwave background supports its existence.

inflaton

The inflaton is a hypothetical scalar field that could drive the period of inflation that took place in the early universe.

interference

Interference is an effect that occurs when two or more waves overlap. In general, the individual waves do not affect one another, and the total wave amplitude at any point in space is simply the sum of the amplitudes of the individual waves at that point. In some places, the two waves may add together, and in other places they may cancel each other out, creating an interference pattern that may look quite different than either of the original waves. Quantum mechanical wavefunctions can interfere, creating interference patterns that can only be observed in their corresponding probability distributions.

ion

An ion is an atom with nonzero electrical charge. A neutral atom becomes an ion when one or more electrons are removed, or if one or more extra electrons become bound to the atom's nucleus.

ionization electron

An ionization electron is a free electron moving at high speed that knocks an electron off a neutral atom, turning the atom into an ion.

isotope

Different atoms of a chemical element in the periodic table all have the same number of protons, but may have a different number of neutrons in their nuclei. These different versions of the same element are called isotopes. The number of neutrons is not simply random, however—the nucleus will only be stable for combinations of protons and neutrons. Most chemical elements have several stable isotopes. For example, lithium (A=3) has two stable isotopes, one with three neutrons in the nucleus (6Li) and one with four (7Li). See: atomic number, mass number.

itinerant

In condensed matter physics, the term itinerant is used to describe particles (or quasiparticles) that travel essentially freely through a material and are not bound to particular sites on the crystal lattice.

jet

In the terminology of particle physics, a jet is a highly directed spray of particles produced and detected in a collider experiment. A jet appears when a heavy quark is produced and decays into a shower of quarks and gluons flying away from the center of the collision.

kaon

The term kaon refers to any one of four mesons with nonzero strangeness. The positively charged K+ is composed of an up quark and an anti-strange quark. Its antiparticle is the negatively charged K– , which is composed of an anti-up quark and a strange quark. The two neutral kaons, and are made of down, anti-down, strange, and anti-strange quarks. CP violation was first observed in the neutral kaon system.

kinetic energy

Kinetic energy is the energy associated with the motion of a particle or system. In classical physics, the total energy is the sum of potential and kinetic energy.

Large Hadron Collider (LHC)

The Large Hadron Collider (LHC) is a particle accelerator operated at CERN on the outskirts of Geneva, Switzerland. The LHC accelerates two counter-propagating beams of protons in the 27 km synchrotron beam tube formerly occupied by Large Electron-Positron Collider (LEP). It is the largest and brightest accelerator in the world, capable of producing proton-proton collisions with a total energy of 14 TeV. Commissioned in 2008–09, the LHC is expected to find the Higgs boson, the last undiscovered particle in the Standard Model, as well as probe physics beyond the Standard Model.

LEP

The Large Electron-Positron Collider (LEP) is a particle accelerator that was operated at CERN on the outskirts of Geneva, Switzerland, from 1989 to 2000. LEP accelerated counterpropagating beams of electrons and positrons in a 27 km diameter synchrotron ring. With a total collision energy of 209 GeV, LEP was the most powerful electron-positron collider ever built. Notably, LEP enabled a precision measurement of the mass of W and Z bosons, which provided solid experimental support for the Standard Model. In 2000, LEP was dismantled to make space for the LHC, which was built in its place.

lepton number

Every lepton in the Standard Model is assigned a lepton number. The electron, muon, and tau and their corresponding neutrinos have a lepton number of 1. Their antiparticle partners have a lepton number of -1. In the Standard Model, lepton number is conserved in all interactions, except in the case of neutrino oscillation.

leptons

The leptons are a family of fundamental particles in the Standard Model. The lepton family has three generations, shown in Unit 1, Fig. 1: the electron and electron neutrino, the muon and muon neutrino, and the tau and tau neutrino.

light curve

The light curve of an astronomical object is a graph of the object's brightness as a function of time. The light curve of a Cepheid variable star rises and falls in a characteristic pattern that looks somewhat like the teeth of a saw, while the light curve of a supernova rises and falls sharply over the course of a few weeks, followed by a long, slow decline.

light-year

A light-year is the distance that light, which moves at a constant speed, travels in one year. One light-year is equivalent to 9.46 x 1015 meters, or 5,878 billion miles.

linac

The term linac is a shortened version of "linear accelerator." A linac is a particle accelerator that accelerates charged particles in a straight line. Charged particles enter the accelerator at one end and are accelerated as they pass through a series of voltages placed along the beam path. Because the path the particles follow is shorter and they pass through fewer accelerating voltages, linacs cannot accelerate particles as much as circular accelerators can. However, linacs are easier to build and run, and they are often used to create beams of particles to be injected into a synchrotron. SLAC is a linac, as were J.J. Thomson's cathode ray tubes.

luminosity

The luminosity of an object is defined as the total energy per unit time emitted by the object. Another term for luminosity is power. For example, the Sun's luminosity, or power output, is 3.8 x 1026 watts.